The Binary Black Hole Alliance was formed to study the collision of black holes and the resulting gravitational radiation by computationally solving Einstein’s equations for general relativity. The location of the black hole surface in a head-on collision has been determined in detail and is described here. The geometrical features that emerge are presented along with an analysis and explanation in terms of the spacetime curvature inherent in the strongly gravitating black hole region. This curvature plays a direct, important, and analytically explicable role in the formation and evolution of the event horizon associated with the surfaces of the black holes.